Some doctors won't do a laparoscopy on a heavy patient, though there are some who will. The risks here are with anesthesia and a slightly elevated chance of perforating something while trying to look around with the scope. A hysteroscopy could be a potential anesthesia problem also, but an IV or a local anesthetic might work out fine.
With a hysterosalpingogram there is a chance that the x-ray machine may have to crowd you a bit, or even touch you, in order to get a good picture. This isn't a big deal, and it doesn't add pain or risk to the test.
Endometrial biopsies shouldn't be any problem, though they aren't very comfortable.
I think the biggest argument against losing weight first is that 95% of people who diet to lose weight gain it back with interest. It would be worse to gain a large amount of weight while pregnant than it would be to start out large.
The other thing is that there is no way to know for sure if you aren't getting pregnant because of your weight or because of something else. Plenty of big women have babies, so it stands to reason that weight alone doesn't disallow pregnancy. You have to decide whether it would be better for you to concentrate on losing weight or finding out what the problem is. If you do opt for losing weight, calculate how long it will take you to reach your goal, and then add a year -- it's a good idea to keep the weight off for a year before getting pregnant. If you decide to move ahead at your current weight, make sure you are eating sensibly and get good medical care.
There are some things you can do for yourself without the help of a doctor.
Chart your basal body temperature (BBT). You need to buy a basal thermometer. A glass one costs about $5, but you have to wait 5 minutes before you get out of bed. For that reason, it is probably better to invest $10 and a B-D digital basal thermometer. These thermometers are more accurate than ones for fever, and accuracy counts for a lot! Once you have one, you should start taking your temp each morning at the same time, before you do any activity (speak, move around, get up, etc.).
Along with this, it is a good idea to chart your other fertility signals such as cervical mucus and cervical position. A wonderful book on the subject is Taking Charge of Your Fertility by Toni Weschler. There is a BBTchart spreadsheet available for download that is tailored toward conception (some fertility awareness charts are geared also toward contraception).
Next, invest in some ovulation predictor kits. OPKs let you know ovulation is about to happen, while BBTs only confirm it after the fact.
Take prenatal vitamins or the equivalent. A multi such as Centrum, combined with additional folic acid (make sure to get at least 800mcg) and calcium should be good.
Think about how you would eat if you were pregnant. Not so much in quantity, but in quality. Try changing your eating plan to be as healthy as you'd want it if your were pregnant, whether or not you are trying to lose weight.
Overweight women often gain less weight than our leaner counterparts during pregnant and that's fine. The main concern is eating properly - not over-eating, and definitely not dieting. Pregnancy is not the time to try to lose weight.
If it makes you feel more comfortable, yes, but only if you are doing it for yourself. It is not something you should feel as if you have to do. Some information out there suggests one should only attempt a 20-pound loss because of the gain-back potential, while others suggest getting down to your goal weight and staying there for a year.